Theoretical Computer Science - Special issue: Fourth workshop on mathematical foundations of programming semantics, Boulder, CO, May 1988
Logical foundations of functional programming
Linear logic, coherence and dinaturality
Selected papers of the 4th summer conference on Category theory and computer science
Games and full completeness for multiplicative linear logic
Journal of Symbolic Logic
Linear logic: its syntax and semantics
Proceedings of the workshop on Advances in linear logic
Locus Solum: From the rules of logic to the logic of rules
Mathematical Structures in Computer Science
Partially additive categories and fully complete models of linear logic
TLCA'01 Proceedings of the 5th international conference on Typed lambda calculi and applications
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We prove a full completeness theorem for MLL without the Mix rule. This is done by interpreting a proof as a dinatural transformation in a *-autonomous category of reflexive topological abelian groups first studied by Barr, denoted ℛ𝒯𝒜. In Section 2, we prove the unique interpretation theorem for a binary provable MLL-sequent. In Section 3, we prove a completeness theorem for binary sequents in MLL without the Mix rule, where we interpret formulas in the category ℛ𝒯𝒜. The theorem is proved by investigating the concrete structure of ℛ𝒯𝒜, especially that arising from Pontrjagin's work on duality.